For the curve given by y equals x squared, what is the average gradient between x = 1 and x = 4?

1. The gradient of a curve changes at every point, so the average gradient is used between two points. 2. The average gradient is the gradient of the straight line through those two points. 3. At x equal to 1 the output is 1 times 1, which is 1, giving the point (1, 1). 4. At x equal to 4 the output is 4 times 4, which is 16, giving the point (4, 16). 5. The vertical change is 16 minus 1, which is 15. 6. The horizontal change is 4 minus 1, which is 3. 7. Dividing 15 by 3 gives an average gradient of 5. 8. Answering 15 stops at the vertical change and never divides by the horizontal change. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 5: Functions_